Theme Essential Question: How can you use formulas and geometry to solve real-world and mathematical problems?
Essential Questions: What is the strategy to find the area of composite figures?
Standards:
7.G. 6 Solve real-world and mathematical problems involving area, volume, and surface area of two-and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms
Objectives:
Review
The student will find area of triangles, rectangles, trapezoids, and parallelograms.
The student will find the area of composite/irregular figures by divide the figures into simple geometric figures and finding the sum of the areas.
Reflections and/or Comments from your PCSSD 7th Grade Curriculum Team
Provide students with ample opportunities to explore and have hands-on experiences with one dimensional figures. Note that Common Core refers to Composite figures while other literature refers to Complex figures.
Background:
Recommended: For a quick overview of the standard(s) to be addressed in this Unit, see Arizona’s Content Standards Reference Materials athttp://www.azed.gov/educator-certification/
Taken from Ohio Dept of Education Mathematics Model Curriculum 6-28-2022
Real-world and mathematical multi-step problems that require finding area, perimeter, volume, surface area of figures composed of triangles, quadrilaterals, polygons, cubes and right prisms should reflect situations relevant to seventh graders. The computations should make use of formulas and involve whole numbers, fractions, decimals, ratios and various units of measure with same system conversions.
The zoo manager has provided the final layout for your animal’s training complex. Complete your scale drawing, provide dimensions that would be suitable for your animal.
Determine the total area for your animal’s training complex. Prepare detail documentation of your calculations.
If the surface covering for the Animal Grazing and Living Area cost $112.35 per square yard, how much will it cost to cover this area? Prepare detail documentation of your calculations.
Key Questions
What is a composite figure?
How do you divide a composite/irregular shaped figure into simpler geometric figures?
How do you find the area of composite/irregular figures?
Observable Student Behaviors (Performance)
The student can use composite/irregular shaped strategies to find area.
Mathematical Practices 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning.
Vocabulary:
Math
Area Composite figures Irregular Area
Suggested Activities:
Houghton Mifflin OnCore Mathematics Middle School Grade 7
Unit 5-3, p. 119-122
ABC Mastering the Common Core in Mathematics
Chapter 11.6. Area of squares and rectangles, p. 135
Chapter 11.7, Area of triangles, p. 136
Chapter 11.8, Area of trapezoids and parallelograms, p. 137
Chapter 11.9, Area of composite figures, p. 138-139
Chapter 11.10, Area Word Problems, p. 140
Chapter 11 Review and Test, p. 146-148
Gizmo Correlation:
7.G.6
Area of Parallelograms-Activity A
Examine and manipulate the graph of a parallelogram or triangle and find its area. Explore the relationship between the area of a parallelogram and the area of a rectangle using an animation.
Rectangle: Perimeter and Area
Resize a rectangle and compare its length, width, and area.
Teaching the Common Core Math Standards with Hands-On Activities,
7.G.6 See Lesson 5-1
Highly Recommended: See Lesson 5-1
The Illustrative Mathematics Project offers guidance to states, assessment consortia, testing companies, and curriculum developers by illustrating the range and types of mathematical work that students will experience in a faithful implementation of the Common Core State Standards. The website features a clickable version of the Common Core in mathematics and the first round of "illustrations" of specific standards with associated classroom tasks and solutions.
JBHM 7th, GP 3, p. 105-160
Glencoe 7th Grade Mathematics Application and Concepts Course 2, Chapter 11-7, p. 498-500
Mathematics in Children's Literature:Many children's books include math concepts and can be used to help teach them in a fun way. This website includes several annotated Lists of Children's Literature including the math concepts and grade levels.
The teaching Channel currently offers videos of K-12 mathematics teaching aligned with the Common Core Sate Standards, which would be perfect for professional development with teacher teams.
Students will practice finding the Circumference, Volume, and Surface Area of given shapes/figures
7.G. 6 Surface Area of Prisms
This lesson will help the students with the formula for lateral area of a prism
7.G. 6 Should I Cover It Up…Or Go Around It?
While looking at geometric shapes in sports, students wll determine whether to find the area or the perimeter for each problem set before them. I have included a football field and a basketball court for challenges. Some sildes require more higher level of learning and more challenging Bloom's Taxonomy questions.
7.G. 6 Measurement Part 1: Area
This lesson activity provides introduces and provides practice in calculating the area of various shapes.
Interactivate is a set of free, online courseware for exploration in science and mathematics. It is comprised of activities, lessons, and discussions. The site is structured around collections of activities, lessons, and discussions.
Content: Solving Area Problems
Dates: 2/19 – 2/22 (4 days)
Theme Essential Question:
How can you use formulas and geometry to solve real-world and mathematical problems?
Essential Questions:
What is the strategy to find the area of composite figures?
Standards:
Objectives:
- Review
The student will find area of triangles, rectangles, trapezoids, and parallelograms.Reflections and/or Comments from your PCSSD 7th Grade Curriculum Team
Provide students with ample opportunities to explore and have hands-on experiences with one dimensional figures. Note that Common Core refers to Composite figures while other literature refers to Complex figures.
Background:
Recommended: For a quick overview of the standard(s) to be addressed in this Unit, see Arizona’s Content Standards Reference Materials athttp://www.azed.gov/educator-certification/
Taken from Ohio Dept of Education Mathematics Model Curriculum 6-28-2022
Real-world and mathematical multi-step problems that require finding area, perimeter, volume, surface area of figures composed of triangles, quadrilaterals, polygons, cubes and right prisms should reflect situations relevant to seventh graders. The computations should make use of formulas and involve whole numbers, fractions, decimals, ratios and various units of measure with same system conversions.
Assessment:
Product
ZOO TRAINER project continues:
Key Questions
Observable Student Behaviors (Performance)
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
Vocabulary:
Suggested Activities:
- Houghton Mifflin OnCore Mathematics Middle School Grade 7
- Unit 5-3, p. 119-122
- ABC Mastering the Common Core in Mathematics
- Chapter 11.6. Area of squares and rectangles, p. 135
- Chapter 11.7, Area of triangles, p. 136
- Chapter 11.8, Area of trapezoids and parallelograms, p. 137
- Chapter 11.9, Area of composite figures, p. 138-139
- Chapter 11.10, Area Word Problems, p. 140
- Chapter 11 Review and Test, p. 146-148
- Gizmo Correlation:
- 7.G.6
- Area of Parallelograms-Activity A
- Examine and manipulate the graph of a parallelogram or triangle and find its area. Explore the relationship between the area of a parallelogram and the area of a rectangle using an animation.
- Rectangle: Perimeter and Area
- Resize a rectangle and compare its length, width, and area.
- Teaching the Common Core Math Standards with Hands-On Activities,
- 7.G.6 See Lesson 5-1
- Highly Recommended: See Lesson 5-1
The Illustrative Mathematics Project offers guidance to states, assessment consortia, testing companies, and curriculum developers by illustrating the range and types of mathematical work that students will experience in a faithful implementation of the Common Core State Standards. The website features a clickable version of the Common Core in mathematics and the first round of "illustrations" of specific standards with associated classroom tasks and solutions.- JBHM 7th, GP 3, p. 105-160
- Glencoe 7th Grade Mathematics Application and Concepts Course 2, Chapter 11-7, p. 498-500
- Glencoe Pre-Algebra, Chapter 3, p. 132-135
- Create a puzzle with unit vocabulary words.
http://www.discoveryeducation.com/free-puzzlemaker/?CFID=1276695&CFTOKEN=75709576Diverse Learners
Homework: (Teachers Discretion)
Terminology for Teachers:
Compoiste Figures = Complex Figures
Ethnicity/Culture | Immigration/Migration | Intercultural Competence | Socialization | Racism/Discrimination
High Yield Strategies
Similarities/Differences | Summarizing/Notetaking| Reinforcing/Recognition| Homework/Practice |
Non-Linguistic representation| Cooperative Learning | Objectives/Feedback |
Generating-Testing Hypothesis | Cues, Questions, Organizers
Resources:
Professional Texts:
Literary Texts
- Geometry and Literature Titles:
http://sci.tamucc.edu/~eyoung/geometry_literature.html- Measurement and children’s Literature/Ratios
http://sci.tamucc.edu/~eyoung/measure_literature.html- Mathematics in Children's Literature:Many children's books include math concepts and can be used to help teach them in a fun way. This website includes several annotated Lists of Children's Literature including the math concepts and grade levels.
Click on the following link, http://libguides.nl.edu/mathinchildrenslit, then look under Math and Literature Bibliographies.- Middle & High School: Literature in Mathematics
Many books include websites with lesson ideas.http://sci.tamucc.edu/~eyoung/middle_school_literature.html
- Lesson Plans for Using Literature in Middle and High School Mathematics (developed by Leonor and edited by Elaine)
http://sci.tamucc.edu/~eyoung/Literature%20webpages/Leonor/index.html- Miscellaneous Math and Children's Literature
http://sci.tamucc.edu/~eyoung/literature.htmlInformational Texts
Art, Music, and Media
Manipulatives:
Games
Videos
SMART Board Lessons, Promethean Lessons
- 7.G. 6 Circumference, Volume, Surface Area
Students will practice finding the Circumference, Volume, and Surface Area of given shapes/figures- 7.G. 6 Surface Area of Prisms
This lesson will help the students with the formula for lateral area of a prism- 7.G. 6 Should I Cover It Up…Or Go Around It?
While looking at geometric shapes in sports, students wll determine whether to find the area or the perimeter for each problem set before them. I have included a football field and a basketball court for challenges. Some sildes require more higher level of learning and more challenging Bloom's Taxonomy questions.- 7.G. 6 Measurement Part 1: Area
This lesson activity provides introduces and provides practice in calculating the area of various shapes.- Smart Board rational number lessons.
http://exchange.smarttech.com/details.html?id=1764f052-3804-448f-9f12-95bc5646a2ea- Rational numbers Smart Board lessons
http://exchange.smarttech.com/details.html?id=050e54ad-0dea-4080-ae54-975d93487209Other Activities, etc.
- Puzzle Maker
- http://www.discoveryeducation.com/free-puzzlemaker/?CFID=1276695&CFTOKEN=75709576
- Interactivate is a set of free, online courseware for exploration in science and mathematics. It is comprised of activities, lessons, and discussions. The site is structured around collections of activities, lessons, and discussions.
http://www.shodor.org/interactivate/guide/Activities and tools:
http://www.shodor.org/interactivate/activities/
Language
Arts
Week 1
Week 2
Week 3
Week 4
Week 5
Week 6
7 Matrix
Accelerated 7
Matrix
Week 1
Week 2
Week 3
Week 4
Week 5
Week 6
Home K-2
Home 3-6
Home 6-8
Unit 1
Unit 2
Unit 3
Unit 4
Unit 5
Unit 6